Question

The general solution of $\tan 5\theta =\cot 3\theta$ is $(n\in Z)$

• A. $\frac{n\pi }{8}+\frac{\pi }{16}$
• B. $\frac{n\pi }{8}$
• C. $\frac{n\pi }{2}+\frac{\pi }{4}$
• D. None of these

Answer 1

Answer: (A)

$\frac{n\pi }{8}+\frac{\pi }{16}$

Given,

$\tan 5\theta =\cot 3\theta$

$\tan 5\theta =\tan (\frac{\pi }{2}-3\theta )$

or, $5\theta =n\pi +\frac{\pi }{2}-3\theta$ [ Where $n\in Z$]

or, $8\theta =n\pi +\frac{\pi }{2}$

or, $\theta =\frac{n\pi }{8}+\frac{\pi }{16}$